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Maths Assertion (A) & Reason (B) MCQ

Number systems · Gujarat Board (GSEB) STD 9 (GSEB - English Medium). 74 questions.

Questions · Page 1 of 2

Assertion (A) & Reason (B) MCQ

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Question 11 Mark
Consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:
  1. Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
  2. Both Assertion (A) and Reason (R) are true but Reason is not a correct explanation of Assertion (A).
  3. Assertion (A) is true and Reason (R) is false.
  4. Assertion (A) is false and Reason (R) is true.
Assertion (A)Reason (R)
e is an irrational number.$\pi$ is an irrational number.
The correct answer is: (a), (b), (c), (d).
Answer
  1. Both Assertion (A) and Reason (R) are true but Reason is not a correct explanation of Assertion (A).
    Solution:
    e and $\pi$ both are irratinoal numbers
    So, both Assertion (A) and Reason (R) are true
    But the Reason (R) is not a correct explanation of Assertion (A), so (b) holds.
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Question 21 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Decimal expansion of every rational number is only terminating.
Reason: Decimal expansion of every irrational number is terminating recurring.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both assertion and reason are false.
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Question 31 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The conjugate of $ 4+\sqrt6$ is $ 4-\sqrt6$
Reason: $\sqrt{27}$ is not a rational number.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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Question 41 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: 199 ÷ 198 = 19
Reason: If a > 0 be a real number and p and q be rational number then ap ÷ aq = ap - q
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 51 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $2+\sqrt6$ is an irrational number.
Reason: Sum of a rational number and an irrational number is always an irrational number.
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
Answer
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
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Question 61 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If a and b are two positive integers then HCF × LCM = a × b.
Reason: A number N Is divided by 15 gives the remainder 2 then the remainder is same when is divided by 5.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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Question 71 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $\sqrt5$ is an irrational number.
Reason: A number is called irrational, if it cannot be written in the form $\frac{\text{p}}{\text{q}},$ where p and q are integers and $\text{q}\neq 0.$
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 81 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $\sqrt2$ is an irrational number.
Reason: A number is called irrational, if it cannot be written in the form $\frac{\text{q}}{\text{p}},$ where p and q are integers and $\text{q}\neq0.$
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
Answer
  1. Assertion is correct statement but Reason is wrong statement.
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Question 91 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Sum of two irrational numbers $5+\sqrt3$ and $7+\sqrt3$ is a irrational number.
Reason: If the product of two irraational numbers is rational the each one is called the rationalizing factor of other.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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Question 101 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: (57)3 = 521
Reason: 9 is a irrational number.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Assertion is true but the reason is false.
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Question 111 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Rational number lying between two rational numbers a and b is $\frac{\text{a}+\text{b}}{2}.$
Reason: There is one rational number lying between any two rational numbers.
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
Answer
  1. Assertion is correct statement but Reason is wrong statement.
    Solution:
    There are infinitely many rational numbers between any two given rational numbers.
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Question 121 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $\frac{7}{8}+\frac{9}{8}=\frac{16}{8}$
Reason: $\frac{\text{p}}{\text{q}}+\frac{\text{r}}{\text{q}}=\text{p}+\frac{\text{r}}{\text{q}}$
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 131 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: 1, 2, 3, 4 are the natural numbers.
Reason: $\frac{1}{4},\frac{2}{7}, \frac{9}{5}$ are the rational numbers.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both assertion and reason are false.
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Question 141 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If  $\sqrt2=1.414.,$ $\sqrt3=1.732,$ then $\sqrt5=\sqrt2+\sqrt3.$
Reason: Square root of a positive real number always exists.
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
Answer
  1. Assertion is wrong statement but Reason is correct statement.
    Solution:
    $=\sqrt2+\sqrt3\neq5$
    $\sqrt3+\sqrt2=1.732+1.414=3.146\neq\sqrt5$ as $\sqrt5=2.236$
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Question 151 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: All whole numbers are rational number except 0.
Reason: am an = am + n
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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Question 161 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The product of two consecutive positive integers is divisible by 2
Reason: The decimal expansion of $\frac{15}{169999}=0.0065789$
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Assertion is true but the reason is false.
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Question 171 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: 2, 3, 5, 7 are the prime numbers.
Reason: A number, other than 1, which is not a prime number is called a composite number.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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Question 181 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Sum of two natural numbers is a natural number.
Reason: All whole numbers are natural numbers.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Assertion is true but the reason is false.
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Question 191 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: A rational number between $\frac{1}{3}$ and $\frac{1}{2}$ is $\frac{5}{12}.$
Reason: Rational number between two numbers a and b is $\sqrt{\text{ab}}.$
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
Answer
  1. Assertion is correct statement but Reason is wrong statement.
    Solution:
    $\frac{1}{2}\Big(\frac{1}{3}+\frac{1}{2}\Big)=\frac{5}{12}$
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Question 201 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $\sqrt2$ is a irrational number.
Reason: It can not be written inthe form of $\frac{\text{p}}{\text{q}}.$
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 211 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Every rational number is written in the form if $\frac{\text{p}}{\text{q}}$ where p and q are integers, q = 0
Reason: $7\sqrt3$ is a rational number.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both assertion and reason are false.
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Question 221 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Coprime number are the number which are the having GCF as1.
Reason: Any two prime numbers does not form the pairs of coprime numbers.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Assertion is true but the reason is false.
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Question 231 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: 7 is rational number
Reason: Square root of all rational number is irrational.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Assertion is true but the reason is false.
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Question 241 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $\sqrt{(7\times8)}=\sqrt7\times\sqrt8$
Reason: $\sqrt{\text{ab}}=\sqrt{\text{a}}\times\sqrt{\text{b}}$
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 251 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $\sqrt2,\sqrt3,$ are examples of irrational numbers.
Reason: An irrational number can be expressed in the form $\frac{\text{p}}{\text{q}}.$
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
Answer
  1. Assertion is correct statement but Reason is wrong statement.
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Question 261 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $32^{\frac{2}{5}}=4$
Reason: $(32)^{\frac{2}{5}}=(2^5)^{\frac{2}{5}}=22=4$
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 271 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: HCF of (23, 53) is 1.
Reason: If p anand are primes, then HCF (p, q) = 1
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 281 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: In 56.49 the whole part is 56.00
Reason: In the number 3456 the place value of 4 is 400
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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Question 291 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: 0.468 is a terminating decimal.
Reason: A decimal in which a digit or a set of digits is repeated periodically, is called a repeating, or a recurring decimal.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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Question 301 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The smallest perfect number is 6, which is the sum of 1, 2, and 3.
Reason: The numbers which are the positive integers and which can be expressed as the sum of their proper divisors are called as perfect number.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 311 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $7\sqrt5,$ $\sqrt2+21$ are the irrational number.
Reason: Every integer is an rational number
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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Question 321 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: 31 is rational number.
Reason: Square root of all rational number is always rational.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Assertion is true but the reason is false.
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Question 331 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: (18, 25) is a pair of coprime numbers.
Reason: pair of coprime number has common factor2.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Assertion is true but the reason is false.
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Question 341 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $\text{x}^4=\frac{\text{X}^5}{\text{x}^1}.$ Reason: $ \frac{\text{a}^{\text{b}}}{\text{a}^{\text{c}}}=\text{a}^{\text{b - c}}.$
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 351 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Every whole number is not a natural number.
Reason: Zero is whole number but not natural number.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 361 Mark
Consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:
  1. Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
  2. Both Assertion (A) and Reason (R) are true but Reason is not a correct explanation of Assertion (A).
  3. Assertion (A) is true and Reason (R) is false.
  4. Assertion (A) is false and Reason (R) is true.
Assertion (A)Reason (R)
$\sqrt{3}$ is an irrational number.Square root a positive integer which is not a perfect square is an irrational number.
The correct answer is: (a), (b), (c), (d).
Answer
  1. Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
    Solution:
    We know that if $\sqrt{\text{x}}$ is an irratinal number, it means x is not a perfect square.
    Thus, Assertion (A) is true
    Since Reason (R) gives Assertion (A), so (a) holds.
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Question 371 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The Decimal fraction of $\frac{12}{125}$ is 0.096
Reason: The Decimal fraction of $\frac{1}{9}$ is 0.111.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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Question 381 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $\frac{1}{6}$ is the reciprocal of 6
Reason: Improper fraction is the fraction in which numerator is less than denominator.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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Question 391 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Natural numbers are a subset of integers.
Reason: Natural numbers without zero are called positive integers, and when written with a negative sign are called as negative integers.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 401 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The terminating decimal has a number of finite terms after the decimal point.
Reason: The decimal expansion of π is terminating.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Assertion is true but the reason is false.
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Question 411 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $5-\sqrt2=5-1.414=3.586$ is an irrational number.
Reason: The difference of a rational number and an irrational number is an irrational number.
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
Answer
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
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Question 421 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: All the rational and irrational number makes up the collection of real number.
Reason: if r is rational and s is irrational then r + s and r - s are irraational number.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 431 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $\frac{10}{3}$ is non terminating Decimal expansion.
Reason: The remainder of non terminating Decimal expansion is never be zero.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 441 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The real number is either rational or irrational.
Reason: $ \sqrt7$ is a rational number.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Assertion is true but the reason is false.
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Question 451 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $ 8\sqrt15\div2\sqrt3=4\sqrt5$
Reason: Quotient of non zero rational number with an irrational number is irrational.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 461 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: 5° = 1
Reason: a° = 1
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Assertion is true but the reason is false.
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Question 471 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $\frac{1}{2}=\frac{3}{6}=\frac{4}{8}$ are the equivalent rational numbers.
Reason: Every rational number is an integer.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Assertion is true but the reason is false.
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Question 481 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: 1 is the multiplicative identity of set of natural number.
Reason: $\sqrt{\text{ab}}=\sqrt{\text{a}}\sqrt{\text{b}}$
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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Question 491 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $ 6\sqrt2+7\sqrt2$ is a rational number.
Reason: The sum of every rational and irrational number is irrational
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 501 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: 0.271 is a terminating decimal and we can express this number as $\frac{271}{1000}$ which is of the form $\frac{\text{p}}{\text{q}}$, where p and q are integers and $q \neq0.$
Reason: A terminating or non - terminating decimal expansion can be expressed as rational number.
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
Answer
  1. Assertion is correct statement but Reason is wrong statement.
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